权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

THE STUDY OF NON-LINEAR PHENOMENA BY THE ASYMPTOTIC ANALYSIS

非线性现象的渐近分析研究

基本信息

批准号：
11640124
负责人：
ITO Masayuki
金额：
$ 2.11万
依托单位：
The University of Tokushima
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640124/
关键词：
quasilinear degenerate elliptic equation eigenvalue problem bifurcation comparison principle difference equation invariant curve degenerate elliptic equation p-Laplacian ∞-Laplacian limit eigenvalue problem delay differential equat

项目摘要

The purpose of this project is to describe nonlinear phenomena mathematically by using asymptotic analysis. And we have the following results.1) Narukawa and Fukagai proposed a mathematical model related to the nonlinear elasticity. This is described by a degenerate quasilinear elliptic equation whose principal part has different orders at 0 and at infinity. They have showed a global bifurcation diagram of positive solutions for a nonlinear eigenvalue problem of such quasilinear equations and, in particular, the coexistence of multiple positive solutions. These results obtained by regularity estimate of weak solutions and modifying the argument given by Ambrosetti, Brezis and Cerami in the semilinear case.2) Ohnuma has investigated a class of singular degenerate parabolic equations including the p-Laplace diffusion equation and the equation of the mean curvature flow, and proved the comparison principle for these equations. He also discovered a strong maximum principle of quasilinear degenerate elliptic equations.3) Murakami showed a necessary and sufficient condition of the asymptotic stability of a fixed point for a higher order linear difference equation. He has also investigated some nonlinear difference equations, derived the formula to compute the stability conditions of the invariant curve caused by the Neimark-Sacker bifurcation and, moreover, given the explicit expression of the invariant curve.4) Kohda has obtained blow-up criteria for a solution of an initial value problem of a semilinear parabolic equation. This is described by using a super-solusion and a sub-solution of the stationary problem. Moreover, he had given some condition which guarantees the blow-up of the solution.

本计画的目的是用渐近分析来描述非线性现象。我们得到了以下结果。1) Narukawa和Fukagai提出了非线性弹性的数学模型。这是用一个退化的拟线性椭圆方程来描述的，它的主成分在0和无穷远处具有不同的阶数。他们给出了一类拟线性方程的非线性特征值问题的正解的全局分岔图，特别是多个正解的共存。这些结果是在半线性情况下，通过对弱解的正则性估计和修正Ambrosetti、Brezis和Cerami给出的论证得到的。2) Ohnuma研究了一类奇异退化抛物型方程，包括p-Laplace扩散方程和平均曲率流方程，并证明了这些方程的比较原理。他还发现了拟线性退化椭圆方程的一个强极大值原理。3) Murakami给出了一类高阶线性差分方程不动点渐近稳定的一个充分必要条件。他还研究了一些非线性差分方程，推导了由neimmark - sacker分岔引起的不变曲线稳定性条件的计算公式，并给出了不变曲线的显式表达式。4) Kohda给出了一类半线性抛物方程初值问题解的爆破判据。这是用平稳问题的超解和子解来描述的。此外，他还给出了保证解的爆破的条件。